Question
Asked Oct 14, 2019
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A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling.

Find an expression for T1, the tension in cable 1, that does not depend on T2.
Express your answer in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g. You must use parentheses around θ1 and θ2, when they are used as arguments to any trigonometric functions in your answer.
Cable 1
Cable 2
m
x
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Cable 1 Cable 2 m x

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Expert Answer

Step 1

The Free body diagram for the arrangement is shown below

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Tr T2 FREE BODY DIAGRAM OFTHE SYSTEM

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Step 2

From the above arrangement if the chandelier is in equilibrium then the vertical and horizontal components of the force must be balanced,

Equating the components along the horizontal x direction,

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T, cos (e,) 7, cos (e,)

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Step 3

Here T1 and T2 are the tensions in the respective strings and θ1 and θ2 are the angles which the connected strings make with the hori...

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T sin (e,)+T, sin (e,)= mg

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